Introduction to Computational Linear Algebra

Chapter 2

Basic Concepts for Matrix

Computations

In Chapter 1, we provided the basics of matrix algebra through the BLAS

operations. In this chapter, we give additional notations and concepts used in

matrix computations. For additional and detailed material on related topics,

we refer the reader to the books by Strang [65], Ciarlet [19], Householder [35]

and Golub and Van Loan [33].

We start by introducing topological structures on the finite dimensional vector

spaces R

n

and C

n

.

2.1 Vector Norms

Vector norms are defined on finite or infinite dimensional vector spaces.

They extend the notion of absolute value (and modulus) on R (and C ). We

proceed as follows. ...